Question

A real estate agent estimates the value of a certain house and lot to be $175,000. If the house is

worth approximately 6.5 times the value of the
lot, how much is each worth separately?

Answer 1

By setting up a system of equations with the given values, we determine the house is approximately worth $151,666.67 and the lot is approximately worth $23,333.33.

Step-by-step explanation:

The task is to determine the separate values of a house and its lot given the total value and the ratio of the house's value to the lot's value. Let's denote the value of the house as H and the value of the lot as L. We are given that the house is worth approximately 6.5 times the value of the lot, so we can present it as H = 6.5L. We are also given that the combined value of the house and the lot is $175,000, so H + L = $175,000. Now we have a system of two equations:

• H = 6.5L
• H + L = $175,000

Substituting the first equation into the second gives us:

• 6.5L + L = $175,000
• 7.5L = $175,000
• L = $175,000 / 7.5
• L = $23,333.33 (approximately)

Now that we know the value of the lot, we can find the value of the house:

• H = 6.5L
• H = 6.5 * $23,333.33
• H = $151,666.67 (approximately)

Therefore, the house is approximately worth $151,666.67 and the lot is approximately worth $23,333.33.